This book presents a theory of measurement, one that is "abstract" in that it is concerned with highly general axiomatizations of empirical and qualitative settings and how these can be represented quantitatively.

This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

-Helps readers apply testing and measurement theories they learn in courses on psychometrics, testing and measurement and/or multivariate statistics taught in psychology, education, marketing and management. -With 22 self-standing modules instructors can pick and choose the ones that are most appropriate for their course. -Each module features an overview of a measurement issue, a step-by-step application of that theory, and two cases which depict typical dilemmas faced when applying measurement theory followed by Questions to Ponder to encourage critical examination of the issues noted in the cases. -Best practices provide recommendations for ensuring the appropriate application of the theory. -Practical questions help students assess their understanding of the topic while the examples allow them to apply the material using real data. -Each module contains exercises some of which require no computer access while others involve the use of SPSS to solve the problem and a continuing exercise incorporates many of the steps in the development of a measure of typical performance. -Recent changes in understanding measurement, with over 50 new and updated references -Explanations of why each chapter, article, or book in each module’s Further Readings section is recommended -Instructors will find suggested answers to the book’s questions and exercises; detailed solutions to the exercises; test bank with 10 multiple choice and 5 short answer questions for each module; and PowerPoint slides. Students and instructors can access SPSS data sets; additional exercises; the glossary; and additional information helpful in understanding psychometric concepts.

This book provides an introduction to measurement theory for non-specialists and puts measurement in the social and behavioural sciences on a firm mathematical foundation. Results are applied to such topics as measurement of utility, psychophysical scaling and decision-making about pollution, energy, transportation and health. The results and questions presented should be of interest to both students and practising mathematicians since the author sets forth an area of mathematics unfamiliar to most mathematicians, but which has many potentially significant applications.

Which types of validity evidence should be considered when determining whether a scale is appropriate for a given measurement situation? What about reliability evidence? Using clear explanations illustrated by examples from across the social and behavioral sciences, this engaging text prepares students to make effective decisions about the selection, administration, scoring, interpretation, and development of measurement instruments. Coverage includes the essential measurement topics of scale development, item writing and analysis, and reliability and validity, as well as more advanced topics such as exploratory and confirmatory factor analysis, item response theory, diagnostic classification models, test bias and fairness, standard setting, and equating. End-of-chapter exercises (with answers) emphasize both computations and conceptual understanding to encourage readers to think critically about the material. ÿ

This book examines test validity in the behavioral, social, and educational sciences by exploring three fundamental problems: measurement, causation and meaning. Psychometric and philosophical perspectives receive attention along with unresolved issues. The authors explore how measurement is conceived from both the classical and modern perspectives. The importance of understanding the underlying concepts as well as the practical challenges of test construction and use receive emphasis throughout. The book summarizes the current state of the test validity theory field. Necessary background on test theory and statistics is presented as a conceptual overview where needed. Each chapter begins with an overview of key material reviewed in previous chapters, concludes with a list of suggested readings, and features boxes with examples that connect theory to practice. These examples reflect actual situations that occurred in psychology, education, and other disciplines in the US and around the globe, bringing theory to life. Critical thinking questions related to the boxed material engage and challenge readers. A few examples include: What is the difference between intelligence and IQ? Can people disagree on issues of value but agree on issues of test validity? Is it possible to ask the same question in two different languages? The first part of the book contrasts theories of measurement as applied to the validity of behavioral science measures.The next part considers causal theories of measurement in relation to alternatives such as behavior domain sampling, and then unpacks the causal approach in terms of alternative theories of causation.The final section explores the meaning and interpretation of test scores as it applies to test validity. Each set of chapters opens with a review of the key theories and literature and concludes with a review of related open questions in test validity theory. Researchers, practitioners and policy makers interested in test validity or developing tests appreciate the book's cutting edge review of test validity. The book also serves as a supplement in graduate or advanced undergraduate courses on test validity, psychometrics, testing or measurement taught in psychology, education, sociology, social work, political science, business, criminal justice and other fields. The book does not assume a background in measurement.

The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM Instrumentation Standard). This text presents an alternative approach. It makes full use of the mathematical theory of evidence to express the uncertainty in measurements. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations. Numerous examples throughout help explain the book’s unique approach.